Question

A small spherical insulator of mass 8.0 × 10^{-2} kg and
charge (left) +0.500 μC is hung by a thin wire of negligible mass.
An identical spherical mass with a negative charge of -1.900 μC
(right) is held 0.20 m away from the sphere and directly to the
right of it, so the wire makes an angle with the vertical (see the
drawing).

What is the magnitude of tension in the wire? (m g/cosθ = 0.813 N)

What is the angle of the string? (tan^{-1} (k
q_{1} q_{2} /m g r^{2}) = 15.3 deg)

**Step 1:** Draw free-body diagrams for the two
spheres in the area above-right (how many forces should each
have?)

**Step 2:** Write down the knowns and unknown
variables.

**Step 3:** Fill in some the blanks: What are the
weights of the two spheres?

What are the vertical and horizontal components of tension in the wire attached to the left sphere?

What is the electrical force (mag and direction) on the left charge as applied by the right charge?

**Step 4:** Sum the Forces (are they in equilibrium
or not?)

∑Fx =

∑Fy =

Answer questions by solving the summation equations:

What is the magnitude of tension in the wire?

What is the angle of the string?

Answer #1

A small spherical insulator of mass 2.91 × 10-2 kg
and charge +0.600 μC is hung by a thin wire of negligible
mass. A charge of -0.900 μC is held 0.150 m away from the
sphere and directly to the right of it, so the wire makes an angle
θ with the vertical (see the drawing). Find (a)
the angle θ and (b) the tension in the wire.

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